SUMMARY OUTPUT
Regression Statistics
Multiple R 0.888950366
R Square 0.790232753
Adjusted R Square 0.764011847
Standard Error 5728.993229
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 9.89E+08 9.89E+08 30.13751 0.000581
Residual 8 2.63E+08 32821363
Total 9 1.25E+09
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%
Intercept -3752.761341 3401.235 -1.10335 0.301955 -11596 4090.5 -11596
X Variable 1 0.329224195 0.059971 5.489764 0.000581 0.190932 0.467517 0.190932
Upper 95.0%
4090.5
0.467517
Look at the data below for the income levels and prices paid for cars for ten people:
Annual Amount
Income Spent on
Level Car
38,000 12,000
40,000 16,000
117,000 41,000
17,000 3,500
23,000 6,500
79,000 21,000
33,000 5,000
66,000 8,000
15,000 1,500
52,000 6,000
Answer the following questions:
A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or ne
B. What is the direction of causality in this relationship - i.e. does having a more expensive car make you earn more money
C. What method do you think would be best for testing the relationship between your dependent and independent variable,
D. Go to this calculation page and enter in your data in the X and Y columns (don't use commas, enter 8,000 as 8000). Then c
(A) We expect a strong, positive correlation between the annual incomes and the amounts spent on cars.
(B) Earning more money makes you spend more on car. Annual income is the X variable and the Amount spent on car is the
(C) Simple Linear Regression is the best method.
(D)
Annual Amount 45,000
Income Spent on 40,000
Level, X Car, Y
35,000
Amount Spent on Car
38,000 12,000
40,000 16,000 30,000
117,000 41,000 25,000
17,000 3,500 20,000
23,000 6,500 15,000
79,000 21,000
10,000
33,000 5,000
5,000
66,000 8,000
0
15,000 1,500
0 20,000 40,000 60,000
52,000 6,000
Annual Income Level
Slope of the regression line is 0.329 and the y- intercept is -3752
The regression equation is Y = 0.329X - 3752
R = 0.8890 confirms that X and Y are strongly correlated. R^2 = 0.7902 means that about 79.02% of the variation in Y is exp
n car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking t
r make you earn more money, or does earning more money make you spend more on your car? In other words, define one of these va
ent and independent variable, ANOVA or regression? Explain your reasoning thoroughly with a discussion of both methods.
, enter 8,000 as 8000). Then click on the button "Y=MX+B". Then click on the "graph" button. Write out your equation as calculated, alo
he Amount spent on car is the Y variable.
y = 0.3292x - 3752.8
60,000 80,000 100,000 120,000 140,000
Annual Income Level
2% of the variation in Y is explained by the variation in X. This is evident from the scatter graph shown above.
onal guess as well as by looking through the data.
her words, define one of these variables as your dependent variable (Y) and one as your independent variable (X).
ion of both methods.
t your equation as calculated, along with your coefficients. Discuss the significance and interpretation of this result, and discuss your grap
variable (X).
of this result, and discuss your graph.